Blockchain Without Waste: Proof-of-Stake
1. Summary
Nothing-at-stake is one of the downsides of Proof-of-Stake. The problem is that the lack of an explicit cost (compared to Proof-of-Work in Bitcoin) coupled with the explicit benefit of the block reward implies that a validator will always update the ledger whenever given the opportunity even if the update necessarily perpetuates disagreement.
This paper examines the nothing-at-stake problem using a formal economic analysis. The key results can be summarized as follows:
Adding a block to the shorter branch on the blockchain has two effects for the player appending the block.
- The first effect is that the player receives a block reward in terms of coins on that branch; this first effect creates an incentive for the player to append the block.
- The second effect is that the value of all coins falls; this second effect competes with the first effect and discourages the player from adding a block to the shorter branch.
A myopic player with no coins always appends to the blockchain when given the option if the block reward takes a strictly positive value. Alternatively, a player with a large stake opts not to append to the blockchain when doing so defers consensus due to the prohibitive cost incurred via her stake being devalued. An equilibrium in which all players follow the Longest Chain Rule exists if each player holds a sufficient stake. In this case, the long chain rule strategy also constitutes a subgame perfect equilibrium. (second effect dominates)
- If there is no block rewards, then there exists an equilibrium in which each player follows the longest chain rule. In other words, a Proof-of-Stake blockchain obtains consensus without further conditions if the blockchain possesses no block reward. (first effect is eliminated)
- The Proof-of-Stake does not lead to wealth concentration. In expectation, one's wealth share remains the same.